Problem: Which of the following ordered pairs represents a solution to the equation below? $(-2, -8) (-1, -4) (0, -3) (1, -1) (2, 2)$ $y = 3x-2$
We can try plugging in the x-value of each ordered pair into the equation. If we evaluate and get the y-value of the ordered pair, then that ordered pair is a solution! Let's consider $(-2, -8)$ If we plug in $-2$ for $x$ and evaluate, do we get $-8$ $y = (3)(-2) - 2 = -6 - 2 = -8$ Let's consider $(-1, -4)$ If we plug in $-1$ for $x$ and evaluate, do we get $-4$ $y = (3)(-1) - 2 = -3 - 2 = -5$ Let's consider $(0, -3)$ If we plug in $0$ for $x$ and evaluate, do we get $-3$ $y = (3)(0) - 2 = 0 - 2 = -2$ Let's consider $(1, -1)$ If we plug in $1$ for $x$ and evaluate, do we get $-1$ $y = (3)(1) - 2 = 3 - 2 = 1$ Let's consider $(2, 2)$ If we plug in $2$ for $x$ and evaluate, do we get $2$ $y = (3)(2) - 2 = 6 - 2 = 4$ Thus the only ordered pair that is a solution to the equation is $(-2, -8)$ We come to the same answer by plotting the points and the equation. $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$ $2$ $4$ $6$ $8$ $\llap{-}4$ $\llap{-}6$ $\llap{-}8$